Type Uniform star polyhedron
Elements F = 54, E = 120
V = 60 (χ = −6)
Faces by sides 30{4}+12{5}+12{5/2}
Wythoff symbol 5/2 5 | 2
Symmetry group Ih, [5,3], *532
Index references U38, C48, W76
Dual polyhedron Medial deltoidal hexecontahedron
Vertex figure
4.5/2.4.5

In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It is given a Schläfli symbol t0,2{5/2,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

## Cartesian coordinates

Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of

(±1/τ2, 0, ±τ2))
(±1, ±1, ±(2τ−1))
(±2, ±1/τ, ±τ)

where τ = (1+5)/2 is the golden ratio (sometimes written φ).

## Related polyhedra

It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the icosidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the square faces in common).

 convex hull Rhombidodecadodecahedron Icosidodecadodecahedron Rhombicosahedron Compound of ten triangular prisms Compound of twenty triangular prisms

### Medial deltoidal hexecontahedron

Medial deltoidal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 54 (χ = −6)
Symmetry group Ih, [5,3], *532
Index references DU38

The medial deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the rhombidodecadodecahedron. It has 60 intersecting quadrilateral faces.